Modelling and Simulation of Entry Objects (Space Debris and Asteroids)

Dr Edmondo Minisci Department of Mechanical and Aerospace Engineering University of Strathclyde, Glasgow, Scotland, UK

Outline

Entry Flows • (Re-)Entry and Hypersonic Flows Hyper. Flows – Introduction to flow regimes and hypersonic phenomena (shock waves and heating)

Space Debris • Re-entry and evolution of Space Debris Intro – Introduction (statistics, hazard & risk assessment) Tools&Met. – Main tools and used methods Our Activ. – Our activities • Entry and evolution of Asteroids/Comets Asteroids Intro – Introduction Methods – Main methods and some recent advances Our Activ. – Our activities

23-June-15 Second talk at University of Cagliari 2 Introduction

Entry Flows • “A space vehicle/object entering the atmosphere of Hyper. Flows a planet passes different flow regimes”, that is “The flow field surrounding a vehicle/object evolves as it descends to the surface of a planet.” Space Debris Intro Tools&Met. • The reason for that lies in: Our Activ. – large entering velocity of the vehicles/objects (≈ 7.5 km/s for re-entry from Earth orbits and 10 km/s for planetary Asteroids entries … up to 20-70 km/s for asteroids/comets), and Intro ≥ Methods – wide range of density and pressure with the altitude. Our Activ.

23-June-15 Second talk at University of Cagliari 3 Introduction

– the large velocity of the entering vehicle/objects (≈ 7.5 km/s for Entry Flows re-entry from Earth orbits and 10 km/s for planetary entries Hyper. Flows … up to 20-70 km/s for asteroids/comets), means evolution ≥ from Space Debris Intro Tools&Met. Hypersonic flow Our Activ. to

Supersonic (not always …) Asteroids and finally Intro Methods Subsonic (not always …) Our Activ.

23-June-15 Second talk at University of Cagliari 4 Introduction The wide range of density and pressure with the Entry Flows altitude, means evolution Hyper. Flows from

Space Debris Free molecular flow Intro to Tools&Met. Our Activ. Disturbed molecular flow (Transition regime) to Asteroids Continuum flow with slip Intro effects Methods to Our Activ. Continuum flow

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Introduction

Entry Flows • The degree of rarefaction is defined by the Knudsen Hyper. Flows number

= Space Debris 휆 Intro • is the molecular mean퐾퐾 free path (average value of Tools&Met. the path length between two퐿 collisions with other Our Activ. molecules)휆

• is the characteristic length scale of the considered Asteroids system Intro 퐿 Methods Our Activ. C. White, 2013.

23-June-15 Second talk at University of Cagliari 6 Introduction

The wide range of The two regimes with continuum Entry Flows density and pressure flow, can be treated with the Hyper. Flows with the altitude, means Navier-Stokes equations and evolution from differ only with respect to the

formulation of the wall boundary Space Debris conditions. Free molecular flow Intro In the nominal case of continuum Tools&Met. to flow no-slip conditions at the wall Our Activ. Disturbed molecular flow are prescribed, whereas in the (Transition regime) second case the flow slips on the to surface Asteroids Continuum flow with slip and the temperature of the wall is Intro effects different from the temperature of the gas at the wall (temperature Methods to Our Activ. jump condition). Continuum flow

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Introduction

The wide range of The two molecular regimes Entry Flows density and pressure require the application/solution of Hyper. Flows with the altitude, means the Boltzmann equations evolution from describing the gas kinetic

behaviour of flows. Boltzmann Space Debris equations, in the context of the Free molecular flow Intro re-entry flow problem, are usually Tools&Met. to solved by methods such as the Our Activ. Disturbed molecular flow Direct Simulation Monte-Carlo (Transition regime) method (DSMC method) to Asteroids Continuum flow with slip Intro effects Methods to Our Activ. Continuum flow

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Introduction

Entry Flows Definition/characterisation of Hyper. Flows hypersonic flows < 1 , subsonic flow (perturbations in the flow propagate both Space Debris 푀downstream∞ and upstream) Intro > 1 , supersonic flow Tools&Met. (perturbations in the flow propagate Our Activ. only푀∞ downstream)

0.8 < < 1.2 , transonic region Asteroids 푀∞ Intro Methods Our Activ. M = speed to sound speed ratio (Mach number)

23-June-15 Second talk at University of Cagliari 9 Introduction

Entry Flows Definition/characterisation of Hyper. Flows hypersonic flows

Shock waves generated for Space Debris > 0.8: Intro Tools&Met. 푀∞ Our Activ. Shock waves are very small regions in the gas where the gas

Asteroids properties change by a large Intro amount. Methods Our Activ.

23-June-15 Second talk at University of Cagliari 10 Hypersonic Flows

Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Across a shock wave, the static pressure, temperature, and gas density increase “very fast”. • Equations for Normal shock waves (shock wave is Space Debris perpendicular to the flow direction) derived by considering the Intro conservation of mass, momentum, and energy for a Tools&Met. compressible gas while ignoring viscous effects. Our Activ.

2 p1 2γM 0 − (γ −1) = p0 γ +1 Asteroids Specific heat ratio, T [2γM 2 − (γ −1)][(γ −1)M 2 + 2] 1.4 Intro 1 = 0 0 (actually 2 2 T0 (γ +1) M 0 function of Methods 훾 ≈ ρ (γ +1)M 2 temperature) Our Activ. 1 = 0 2 ρ0 (γ −1)M 0 + 2

23-June-15 Second talk at University of Cagliari 11 Hypersonic Flows

Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Since shock waves do no work, and there is no heat addition, the total enthalpy and the total temperature are constant. • Since the flow is non-isentropic, the total pressure downstream Space Debris of the shock is always less than the total pressure upstream of Intro the shock. Tools&Met. • Equations for Normal shock waves (shock wave is Our Activ. perpendicular to the flow direction) derived by considering the

conservation of mass, momentum, and energy for a

Asteroids compressible gas while ignoring viscous effects. γ 1 Intro p  (γ +1)M 2  γ −1  γ +1  γ −1 t1 = 0 Methods  2   2  pt0 (γ −1)M 0 + 2 2γM 0 − (γ −1) Our Activ. T t1 =1 Tt0

23-June-15 Second talk at University of Cagliari 12 Hypersonic Flows

Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • The Mach number and speed of the flow also decrease across a shock wave. • Equations for Normal shock waves (shock wave is Space Debris perpendicular to the flow direction) derived by considering the Intro conservation of mass, momentum, and energy for a Tools&Met. compressible gas while ignoring viscous effects. Our Activ.

2 2 (γ −1)M 0 + 2 Asteroids M1 = 2γM 2 − (γ −1) Intro 0 Methods Our Activ.

23-June-15 Second talk at University of Cagliari 13 Space Debris Re-entry

• Aerodynamic loads Entry Flows • Aerodynamic force and torque are the resulting action of Hyper. Flows pressure and shear stress distribution over the object surface  ρV 2   = + Space Debris Fa ∫ (cPn cτ t )dS Intro 2 S Tools&Met.  ρV 2     Our Activ. M = (r ×c n + r ×cτ t )dS a 2 ∫ P S 2 • q=pV /2 dynamic free stream pressure, cP = p/q local Asteroids pressure coeff., c = /q local shear stress coeff., , Intro surface unit normal and tangential vectors on local Methods surface element, 휏dS,휏 the vector distance to the centre� of Our Activ. mass.푡⃗ 푟⃗

23-June-15 Second talk at University of Cagliari 14 Space Debris Re-entry

Entry Flows • Aerodynamic loads Hyper. Flows • Aerodynamic force and torque are the resulting action of pressure and shear stress distribution over

Space Debris the object surface (long. plane) Intro Tools&Met. 2 2 Our Activ. ρV ρV L = CL S ; D = CD S 2 2 2 Asteroids ρV M = CM cS Intro 2 Methods Our Activ.

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Entry Flows • Definition/characterisation of hypersonic flows Hyper. Flows • Change from subsonic to supersonic conditions is quite sharp.

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

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Entry Flows • Definition/characterisation of hypersonic flows Hyper. Flows • Hypersonic aerodynamics is much different than the now conventional and experienced regime of Space Debris Intro supersonic aerodynamic. Tools&Met. • “Rule of thumb”: hypersonic if Mach number >5 Our Activ. • Hypersonic flow is best defined as the regime where

certain physical phenomena become progressively Asteroids more important as the Mach number is increased to Intro higher values (some phenomena may become Methods important before reaching 5, other much after … no Our Activ. crisp threshold)

J. Anderson, HYPERSONIC AND HIGH TEMPERATURE GAS DYNAMICS, McGraw-Hill Book, 1989.

23-June-15 Second talk at University of Cagliari 17 Hypersonic Flows

• Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Thin shock layers The flow field between the shock wave and the body is defined as the Space Debris shock layer, and for hypersonic speeds this shock layer can be quite Intro thin. Tools&Met. Some physical complications, such as the merging of the shock wave Our Activ. itself with a thick, viscous boundary layer growing from the body surface.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 18 Hypersonic Flows

Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows Viscous interaction Viscous dissipation: high kinetic energy is transformed (in part) into internal energy. Space Debris The characteristics of hypersonic boundary layers are dominated Intro by temperature increases. Tools&Met. – The viscosity increases with temperature, and this by itself will make the Our Activ. boundary layer thicker; – because the pressure p is constant in the normal direction through a boundary layer, the increase in temperature T results in a decrease in

density: in order to pass the required mass flow through the boundary layer Asteroids at reduced density, the boundary-layer thickness must be larger. Intro Both of these phenomena combine to make hypersonic boundary Methods layers grow more rapidly than at slower speeds. (“Change of Our Activ. shape”)

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Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows High temperature flows The vibrational energy of the molecules becomes excited, and

this causes the specific heats cp and cv. to become functions of Space Debris temperature. Intro Tools&Met. In turn, the ratio of specific heats, = cp/cv also becomes a Our Activ. function of temperature. 훾 For air. this effect becomes important above a temperature of 800 K. Asteroids As the gas temperature is further increased, chemical reactions Intro can occur. Methods Our Activ. For an equilibrium chemically reacting gas cp and cv are functions of both temperature and pressure, and hence =f(T, p).

훾 23-June-15 Second talk at University of Cagliari 20 Hypersonic Flows

Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows High temperature flows

For air at 1 atm pressure, Oxygen dissociation (O2 -> Space Debris 2O) begins at about 2000 K, and the molecular oxygen Intro is essentially totally dissociated at 4000 K. Tools&Met. Our Activ. At 4000 K N2 dissociation (N2 -> 2N) begins, and is essentially totally dissociated at 9000 K.

Asteroids Above a temperature of 9000 K, ions arc formed (N -> + - + - Intro N + e , and O -> O + e ), and the gas becomes a Methods partially ionized plasma. Our Activ.

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Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows High temperature flows

The gas temperature behind the strong shock wave can be

enormous at hypersonic speeds. Space Debris

Intro 1. temperature in the nose region of Tools&Met. a hypersonic object can be Our Activ. extremely high; 2. The proper inclusion of chemically reacting effects is vital to the Asteroids calculation of an accurate shock- Intro layer temperature; the

Methods assumption that the ratio of

Our Activ. specific heats = cp/cvis constant and equal to 1.4 is no longer valid. 훾

23-June-15 Second talk at University of Cagliari 22 Hypersonic Flows

Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows High temperature flows High-temperature chemically reacting flows can have an Space Debris influence on aerodynamic characteristics (lift, drag, and Intro moments) on a hypersonic vehicle/object. Tools&Met. Our Activ. For example, such effects have been found to be important to estimate the amount of body-flap deflection necessary to trim the space shuttle during high-speed re-entry. Asteroids Intro However, by far the most dominant aspect of high Methods temperatures in hypersonics is the resultant high heat- Our Activ. transfer rates to the surface.

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Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows High temperature flows

This aerodynamic heating takes the form of heat transfer from the hot boundary layer to the cooler surface, called Space Debris convective heating, and denoted by qc . Intro Moreover, if the shock-layer temperature is high enough, Tools&Met. the thermal radiation emitted by the gas itself can become Our Activ. important, giving rise to a radiative flux to the surface

called radiative heating, and denoted by qr • Example, for Apollo reentry, radiative heat transfer was Asteroids more than 30 % of the total heating, while Intro • for a space probe entering the atmosphere of Jupiter, the Methods radiative heating will be more than 95 % of the total Our Activ. heating.

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Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows High temperature flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 25 Hypersonic Flows Aero-thermodynamic Entry Flows characteristics Hyper. Flows CFD (Integrated Navier–

Stokes equations solutions) Space Debris for continuum Intro Tools&Met. Our Activ.

Asteroids Intro DSMC (solution to the Methods Our Activ. Boltzmann equation) for molecular regimes

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Aero-thermodynamic characteristics Entry Flows Hyper. Flows Pressure distribution Local heat flux

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

Wuilbercq et All, 2012 23-June-15 Second talk at University of Cagliari 27 Hypersonic Flows

Newtonian Theory for pressure distribution Entry Flows Hyper. Flows According to newtonian model: • the flow consists of a large number of individual particles impacting the surface and then moving tangentially to it Space Debris • At collision with the surface, the particles lose their component Intro of momentum normal to the surface, but the tangential Tools&Met. component is preserved. Our Activ. • Force on the surface = time rate of change of the normal component of momentum

Asteroids Intro Methods Our Activ.

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Entry Flows Newtonian Theory for pressure distribution Hyper. Flows • Force on the surface = time rate of change of the normal component of momentum

Space Debris • Time rate of change of momentum (normal Intro 2 2 component) is: (ρ∞V∞ Asinθ )(V∞ sinθ ) = ρ∞V∞ Asin θ Tools&Met. nd 2 2 Our Activ. • For the 2 Newton’s law N = ρ∞V∞ Asin θ

Asteroids Intro Methods Our Activ.

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Entry Flows • Newtonian Theory for pressure distribution Hyper. Flows nd 2 2 • For the 2 Newton’s law N = ρ∞V∞ Asin θ N 2 2 = ρ∞V∞ sin θ • Force per unit area A 2 2 Space Debris − = ρ θ • Pressure difference p p∞ ∞V∞ sin Intro Tools&Met. Our Activ. p − p C = ∞ = 2sin 2 θ p 1 ρ V 2 2 ∞ ∞ Asteroids Intro Methods Our Activ.

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Entry Flows Newtonian Theory for pressure distribution Hyper. Flows • Modified newtonian theory (more accurate for calculation of pressure coefficients around blunt

Space Debris bodies)

Intro Tools&Met. Our Activ. 2 C p = C p,max sin θ

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 31 SPACE DEBRIS RE-ENTRY

• The lifetime of objects in low Earth orbits (LEO) is limited due to Entry Flows the atmospheric drag. Hyper. Flows

• Generally, these objects demise, but surviving fragments of Space Debris heavy re-entry objects can cause a non-negligible risk to the Intro ground population. Tools&Met.

Our Activ.

Asteroids Intro Methods Our Activ. Delta (Photo:NASA)

23-June-15 Second talk at University of Cagliari 33 Space Debris Re-entry

• Re-entry statistics Entry Flows • Since the decay of the Sputnik 1 launch vehicle core stage on Hyper. Flows December 1957, near 22 000/25 000 catalogued orbiting objects have re-entered the Earth’s atmosphere

Space Debris • More than 5,400 metric tons of materials are believed to have Intro survived re-entry with no major reported casualties Tools&Met. Our Activ. • Largest object to re-enter was the Russian Mir Space Station, which weighed 135,000 kg which was controlled re-entry in the year 2001

Asteroids • Other large-scale re-entry events were: Skylab (74 tones, July Intro 1979), Salyut-7/Kosmos-1686 (40 tones, February 1991), and Methods Upper Atmosphere Research Satellite (UARS) (5.5 tones, Our Activ. September 2011).

23-June-15 Second talk at University of Cagliari 34 Space Debris Re-entry

• Re-entry statistics Entry Flows Hyper. Flows • Generally, about 10-40 percent of a satellite’s mass will survive re-entry. • The actual percentage for a specific object depends on the Space Debris materials used in the object’s construction, shape, size, and Intro weight of the re-entering object. Tools&Met. Our Activ.

Asteroids Object recovered from the re-entry of the Delta Intro second Methods stage into Texas was this Our Activ. 250-kg propellant tank (Photo:NASA)

23-June-15 Second talk at University of Cagliari 35 Space Debris Re-entry

• A satellite in circular orbit approaching the re-entry in the Entry Flows atmosphere has a specific mechanical energy of ∼3.1 e7 J/kg. Hyper. Flows • If all this energy were converted into heat entirely absorbed by

the body, most material would be totally vaporized.

Space Debris Intro Enthalpies of vaporization of common substances, measured at their Tools&Met. respective standard boiling points: (J/kg) Our Activ. Aluminium 10.5 e6 Iron 6.09 e6 Water 2.26 e6 Asteroids • However, only a small fraction of the energy theoretically Intro available is converted into heat absorbed by the body Methods Our Activ. • The chance of having surviving satellite components hitting the ground is quite high

23-June-15 Second talk at University of Cagliari 36 Space Debris Re-entry

Entry Flows • Structurally loose components characterized by a Hyper. Flows high area to mass ratio (e.g. solar panels or large antennae) are generally lost at an altitude around 100 km, Space Debris • Most spacecraft and upper stages mainly Intro disintegrate at an altitude of about 78(±10) km, due Tools&Met. Our Activ. to the heat and the dynamic loads of the re entry. • The survivability of specific components depends on a numbers of factors: structure, composition, shape, Asteroids area to mass ratio, release sequence and shielding Intro from other parts of the system during the critical Methods Our Activ. phases of maximum heating.

23-June-15 Second talk at University of Cagliari 37 Space Debris Re-entry

Entry Flows • Surviving fragments of heavy re-entry objects can Hyper. Flows cause a non-negligible risk to the ground population.

Space Debris Intro • Space debris mitigation standards specify upper Tools&Met. limits for the acceptable risk. Our Activ. ( NASA-STD-8719.14A )

Asteroids Intro • Re-entry analysis tools verify the compliance with Methods the applicable standards Our Activ.

23-June-15 Second talk at University of Cagliari 38 Space Debris Re-entry

Entry Flows • Hazard and risk assessment (NASA-STD-8719.14A ) Hyper. Flows • Transfer of an orbital environment risk to a potential human casualty risk.

• The potential human casualty risk includes all prompt Space Debris Intro injuries due to the impact from falling debris as well as Tools&Met. exposures to hazardous materials which include Our Activ. chemical, explosive, biological, and radiological materials.

Asteroids • The potential for human casualty is assumed for any Intro object with an impacting kinetic energy in excess of 15 Methods J (widely accepted as the minimum level for potential Our Activ. injury to an unprotected person)

23-June-15 Second talk at University of Cagliari 39 Space Debris Re-entry

Entry Flows • Hazard and risk assessment (NASA-STD- Hyper. Flows 8719.14A )

Space Debris • For uncontrolled reentry, the risk of human Intro casualty from surviving debris shall not exceed Tools&Met. 0.0001 (1:104) Our Activ.

Asteroids • ESA has also proposed and adopted a reentry Intro human casualty risk threshold of 1 in 10,000. Methods Our Activ.

23-June-15 Second talk at University of Cagliari 40 Space Debris Re-entry

• Hazard and risk assessment (NASA-STD-8719.14A ) Entry Flows Hyper. Flows • In order to evaluate the hazard and ground risk due to a single surviving debris, the safety standard introduces an Space Debris equivalent casualty area DAi of a single debris, which is Intro composed of the cross-section area Ai of the debris and a Tools&Met. 2 projected human risk cross-section area of Ah=0.36 m , Our Activ. 2 DAi = ( Ah + Ai )

Asteroids • The total casualty area Ac of a reentry event is the Intro summation over all surviving fragments, n 2 Methods Our Activ. DA = ∑( Ah + Ai ) i=1

23-June-15 Second talk at University of Cagliari 41 Space Debris Re-entry

Entry Flows • Hazard and risk assessment Hyper. Flows

• Total human casualty expectation, E, can then be Space Debris defined as Intro Tools&Met. E = D x P Our Activ. A D

• where PD is equal to the average population density Asteroids for the particular orbital inclination and year of Intro Methods reentry. Our Activ.

23-June-15 Second talk at University of Cagliari 42 Space Debris Re-entry

Entry Flows • Re-entry analysis tools verify the compliance with the Hyper. Flows applicable standards

• Some commonly used reentry analysis tools, are: Space Debris Intro Tools&Met. • NASA’s DAS (Debris Assessment Software) and Our Activ. ORSAT (Object Re-entry Survival Analysis Tool), and

Asteroids • ESA’s re-entry analysis module SESAM (Spacecraft Intro Entry Survival Analysis Module) and SCARAB Methods (Spacecraft Atmospheric Re-entry and Aerothermal Our Activ. Breakup)

23-June-15 Second talk at University of Cagliari 43 Space Debris Re-entry

Entry Flows • A complete analysis system for spacecraft Hyper. Flows destruction requires a multi-disciplinary software system in which the various analysis modules continuously exchange the individual results for a Space Debris Intro stepwise analysis of the spacecraft re-entry and the Tools&Met. resulting destruction. Our Activ.

• The destruction analysis of a spacecraft during its re- Asteroids entry first requires the geometric and physical Intro Methods models of the spacecraft and of its elements. Our Activ.

23-June-15 Second talk at University of Cagliari 44 Space Debris Re-entry

Entry Flows • In order to treat the evolution (destruction) during re-entry Hyper. Flows the following aspects have to be modelled:

• flight dynamics of the object, Space Debris Intro • aerodynamic and aero-thermal loads, Tools&Met. • (dynamic) spacecraft behaviour under the external loads, Our Activ. • local heating and the resulting melting process (thermal model) Asteroids • mechanical loads and the relevant fragmentation or Intro deformation processes, Methods Our Activ. • fragment tracking till ground impact

23-June-15 Second talk at University of Cagliari 45 Space Debris Re-entry

Entry Flows • Flight dynamics of the object Hyper. Flows • In general, the trajectory and attitude motion of each object is determined by numerical integration of the

Space Debris 3-6 DOF equations of motion, describing the change Intro of momentum (3DOFs) and angular momentum Tools&Met. (additional 3DOFs) of the spacecraft under the action Our Activ. of external forces (3DOFs) and torques (additional 3DOF)   Asteroids d (mV )= Fext Intro dt Methods d   Our Activ. (Iω) = M dt ext

23-June-15 Second talk at University of Cagliari 46 Space Debris Re-entry

23-June-15 Second talk at University of Cagliari 47 Space Debris Re-entry

Entry Flows • Aerodynamic loads Hyper. Flows • Aerodynamic force and torque are the resulting action of pressure and shear stress distribution over

Space Debris the object surface (long. plane) Intro Tools&Met. 2 2 Our Activ. ρV ρV L = CL S ; D = CD S 2 2 2 Asteroids ρV M = CM cS Intro 2 Methods Our Activ.

23-June-15 Second talk at University of Cagliari 48 Space Debris Re-entry dr = vsin γ dt dλ v cosγ sin χ Spherical rotating = Entry Flows dt r cosδ planet dδ v cosγ cos χ Hyper. Flows = dt r dv − D = −g sinγ + + Space Debris dt m Intro 2 +ωE r cosδ (cosδ sin γ − sinδ cosγ cos χ) Tools&Met. Our Activ. dχ v cosγ = sin χ sinδ + dt r cosδ 2 ωE r cosδ + 2ωE (sinδ − tanγ cosδ cos χ) + sin χ sinδ Asteroids v cosγ Intro dγ g L v cosγ Methods = − cosγ + + + dt v mv r Our Activ. ω 2 r cosδ + 2ω sin χ cosδ + E (cosδ cosγ + sin γ sinδ cos χ) E v

23-June-15 Second talk at University of Cagliari 49 Space Debris Re-entry Spherical non-rotating dV ρSC V 2 planet Entry Flows = − D − g sin(γ ) Hyper. Flows dt 2m

dγ V g  1 ρSC V 2 =  −  cos(γ )+ L Space Debris dt  r V  V 2m Intro dh Tools&Met. = V sin(γ ) Our Activ. dt dθ V m m = cos(γ ) βm = α m =

dt r S CD S CL Asteroids Intro Ballistic factor Lift factor Methods Our Activ.

23-June-15 Second talk at University of Cagliari 50 Space Debris Re-entry

Entry Flows • Aero-thermal loads Hyper. Flows • The aero-thermal analysis predicts the convective heat transfer to the outer surface of the space object

Space Debris based on the aerodynamic and free stream Intro conditions provided by the aerodynamic and flight Tools&Met. dynamic calculation, respectively. Our Activ.

• Mechanical loads and the relevant Asteroids Intro fragmentation/deformation processes Methods • Simplified analysis, restricted to fracture of joints Our Activ. between some elementary parts of the space object..

23-June-15 Second talk at University of Cagliari 51 Space Debris Re-entry

• The available analysis methods can be divided into the Entry Flows following two categories: Hyper. Flows • object-oriented codes, • spacecraft-oriented codes. Space Debris Intro Tools&Met. • Object-oriented methods analyse only individual Our Activ. parts of the spacecraft. • These methods usually assume that at a certain altitude the spacecraft is decomposed into its individual elements. Asteroids For each critical element of the decomposed spacecraft a Intro destructive re-entry analysis is then performed. Methods • (DAS, ORSAT, SESAM) Our Activ.

23-June-15 Second talk at University of Cagliari 52 Space Debris Re-entry

• The available analysis methods can be divided into the Entry Flows following two categories: Hyper. Flows • object-oriented codes,

• spacecraft-oriented codes. Space Debris Intro • Spacecraft-oriented codes model the complete Tools&Met. spacecraft as close as possible to the real design as Our Activ. one consistent object. • Aerodynamic and aero-thermodynamic coefficients are calculated for the real, complex geometric shape, and not Asteroids for simplified object shapes. Breakup events are Intro computed by analysing the actually acting mechanical Methods and thermal loads (i.e. breaking or melting into two more fragments). Shadowing and protection of spacecraft parts Our Activ. by others are taken into account.

23-June-15 Second talk at University of Cagliari 53 Space Debris Re-entry

Why Object oriented methods? Entry Flows Hyper. Flows Object-oriented methods reduce the re-entry analysis of a complete spacecraft to the individual destruction analysis of its critical parts. The concept of a fixed, common breakup altitude Space Debris usually in the range [75, 85] (km), allows determining a ground Intro impact footprint for the surviving debris objects. Tools&Met. Our Activ. This footprint depends on

breakup conditions Asteroids (position, altitude, velocity Intro vector) and on the ballistic Methods coefficients of the debris Our Activ. objects. (C) (Lips et All, 2005)

23-June-15 Second talk at University of Cagliari 54 Space Debris Re-entry

Entry Flows Hyper. Flows Assumption that the individual destructive re-entry Space Debris of the spacecraft Intro parts only starts at Tools&Met. the breakup Our Activ. altitude, which a priori is unknown => generally prediction Asteroids of a higher ground risk. Intro Methods Our Activ. (C) (Lips et All, 2005)

23-June-15 Second talk at University of Cagliari 55 Space Debris Re-entry

Entry Flows • Thus object-oriented codes can (in principle) be used Hyper. Flows to predict a possible range of the ground risk.

Space Debris • The minimum ground risk margin is given with high Intro confidence by a full re-entry analysis. The upper Tools&Met. margin for the ground risk will strongly depend on the Our Activ. assumed breakup altitude.

Asteroids Intro • The ground risk will increase with decreasing Methods breakup altitude. Our Activ.

23-June-15 Second talk at University of Cagliari 56 Space Debris Re-entry

Entry Flows • DAS (Developed by Lockheed in 1998) Hyper. Flows • The spacecraft to be analysed is modelled as a set of geometric objects (spheres, cylinders, boxes, and Space Debris Intro flat plates). Tools&Met. Our Activ. • Each object is defined by its shape, geometric

dimensions, mass, and material. Asteroids Intro • For thermal analysis DAS uses a lumped thermal Methods mass model for solid objects only. Our Activ.

23-June-15 Second talk at University of Cagliari 57 Space Debris Re-entry

• DAS Entry Flows • For thermal analysis DAS uses a lumped thermal mass Hyper. Flows model for solid objects only.

Temperature variations within the Space Debris mass can be neglected in comparison with the temperature Intro difference between the mass and Tools&Met. the surroundings Our Activ. • Hollow objects with finite wall thickness or objects consisting of several different materials have to be Asteroids modelled by an effective density approach. Intro • Assumption: an object demises when the accumulated Methods heat input reaches the material heat of ablation (melting) Our Activ.

23-June-15 Second talk at University of Cagliari 58 Space Debris Re-entry

Entry Flows • DAS Hyper. Flows

• Not able to predict partial melting and fragmentation Space Debris of objects (more conservative approach, i.e. DAS Intro predicts no destruction at all for objects which would Tools&Met. be partially molten in reality ... very conservative) Our Activ.

Asteroids • All material properties in the material database of Intro DAS are assumed to be temperature independent. Methods The emissivity in DAS is constant, 1.0 for all Our Activ. materials.

23-June-15 Second talk at University of Cagliari 59 Space Debris Re-entry

Entry Flows • DAS Hyper. Flows • The main output of a re-entry analysis with DAS is a table with the resulting demise altitudes or the Space Debris Intro calculated casualty areas for each ground impacting Tools&Met. object. Our Activ.

• DAS should be used for first risk assessments. If the Asteroids predicted risk on ground is not acceptable a more Intro accurate tool should be used in order to verify the Methods results of DAS (procedure according to NASA Safety Our Activ. Standard).

23-June-15 Second talk at University of Cagliari 60 Space Debris Re-entry

Entry Flows • ORSAT (Developed by the NASA Lyndon B. Hyper. Flows Johnson Space Center - original version release in 1993)

Space Debris • Similar to DAS, ORSAT analyses the thermal Intro destruction by melting during a ballistic re-entry for Tools&Met. selected shapes of bodies and object motion Our Activ. assumptions.

Asteroids Intro (Lips and Fritsche, 2005) Methods Our Activ.

23-June-15 Second talk at University of Cagliari 61 Space Debris Re-entry

• ORSAT Entry Flows Hyper. Flows • It considers thermal heating based on the lumped mass approach or one-dimensional heat conduction Space Debris Intro Tools&Met. • Partial melting of objects is considered by a demise Our Activ. factor.

• Almost all material properties in the material database of Asteroids ORSAT are temperature dependent. Intro

Methods Our Activ. • Heating by oxidation is considered.

23-June-15 Second talk at University of Cagliari 62 Space Debris Re-entry

• ORSAT Entry Flows Hyper. Flows • Limited to a ballistic, non-lifting re-entry, then only tumbling motions or stable orientations of the body are Space Debris allowed Intro Tools&Met. Our Activ. • For boxes, cylinders, plates these are head-on, broadside or normal-to-flow orientations.

Asteroids • Due to the three-dimensional ballistic flight dynamics Intro model the aerodynamic analysis has to provide only the Methods drag coefficient. The aerodynamic analysis is based on Our Activ. the hypersonic limit Ma>>1

23-June-15 Second talk at University of Cagliari 63 Space Debris Re-entry

• ORSAT Entry Flows

Hyper. Flows • A distinction is made between the three flow regimes: • Hypersonic Free molecular flow CDfm = f (Shape, Motion), Space Debris • Hypersonic Rarefied transitional flow CDtrans = f (Shape, Intro Motion, Kn), Tools&Met. • Hypersonic Continuum flow CDcont = f (Shape, Motion). Our Activ. • A Knudsen number dependent bridging function is applied in the transitional flow regime: Asteroids Intro • = 3 Methods + 0.5 + 0. 퐷𝐷퐷�퐷 Our Activ. 퐶 • 퐷퐷퐷 퐷𝐷𝐷 퐶 �퐶퐶𝐶 퐶 − 퐶 �푠� 휋 25푙푙𝑙

23-June-15 Second talk at University of Cagliari 64 Space Debris Re-entry

Entry Flows • ORSAT Hyper. Flows • A Knudsen number dependent bridging function is applied in the transitional flow regime:

Space Debris • = Intro + 0.5 + 0. 3 Tools&Met. 퐶퐷𝐷퐷�퐷 Our Activ. 퐶퐷𝐷𝐷 퐶퐷퐷퐷 − 퐶퐷𝐷𝐷 �푠� 휋 25푙푙𝑙 •

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 65 Space Debris Re-entry

• ORSAT Entry Flows • The aero-heating law also distinguishes between the three flow Hyper. Flows regimes. An averaged shape and motion dependent heat flux to

the surface is assumed.

Space Debris • In hypersonic continuum flow the heat transfer formula for a spherical stagnation point of Detra, Kemp, Riddell is used as Intro the primary basis. Tools&Met. . Our Activ. • = [W m-2] ( / ) 110 285 휌∞ 푉∞ 3 15 • In𝑠𝑠𝑠 free molecular푛 푠푠flow:푐푐푐푐 푐푐푐푐 푞̇ 푅 휌 푉 푉 ≈ 7900� � Asteroids = • 3 ( T thermal accommodation coefficient, =0.9) Intro 훼푇휌∞푉∞ • Shape𝑠𝑠 -dependent effective radii of curvature and motion- Methods 푞̇ 2 훼 Our Activ. dependent averaging factors are applied in order to use these equations for all object shapes and motion.

23-June-15 Second talk at University of Cagliari 66 Space Debris Re-entry

Entry Flows • ORSAT Hyper. Flows • The aero-heating law also distinguishes between the three flow regimes. An averaged shape and motion

Space Debris dependent heat flux to the surface is assumed. Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ. (Lips and Fritsche, 2005)

23-June-15 Second talk at University of Cagliari 67 Space Debris Re-entry

Entry Flows • ORSAT Hyper. Flows • Stanton number, St is the ratio of heat transferred to the thermal capacity of fluid α St = Space Debris ρVcp Intro • where, = convection heat transfer coefficient, ρ = Tools&Met. Our Activ. density of the fluid, cp = specific heat of the fluid, V = speed of훼 the fluid

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 68 Space Debris Re-entry

Entry Flows • ORSAT Hyper. Flows

• The atmosphere model in ORSAT is the US Space Debris Standard Atmosphere 1976. Intro Tools&Met. Our Activ. • The Mass Spectrometer Incoherent Scattering Extended-1990 (MSISe-90) model is also available.

Asteroids (There are only small differences between both Intro models in the altitude regime below 120 km.) Methods Our Activ.

23-June-15 Second talk at University of Cagliari 69 Space Debris Re-entry

• ORSAT Entry Flows Hyper. Flows • ORSAT also provides the possibility to define multiple breakup altitudes and the concept of aerodynamic and thermal mass. Space Debris Intro Tools&Met. • The aerodynamic mass is used for trajectory calculation Our Activ. whereas the thermal mass is used for the heating analysis. Due to this approach, heavy parent objects (aerodynamic mass) with light weighted shells (thermal Asteroids mass) can be analysed until the demise of the shells. Intro Methods • Internal parts can be exposed to the flow subsequently at Our Activ. several calculated breakup altitudes.

23-June-15 Second talk at University of Cagliari 70 Space Debris Re-entry

Entry Flows • ORSAT Hyper. Flows • Some more recent upgrades of ORSAT include:

Space Debris • Fay–Riddell heating algorithm with hot gas effects, Intro Tools&Met. • one-dimensional heat conduction in boxes and flat Our Activ. plates,

• radiative heat exchange between an outer object Asteroids (e.g. housing) enclosing an internal component (e.g. Intro electronic box), Methods Our Activ. • drag coefficients at low Mach numbers.

23-June-15 Second talk at University of Cagliari 71 Space Debris Re-entry

• SCARAB Entry Flows • Spacecraft oriented code Hyper. Flows

• Developed by Hypersonic Technology Göttingen (HTG) Space Debris since 1995 within the frame of several ESA/ESOC Intro contracts Tools&Met. Our Activ. • Aerodynamic and aero-thermodynamic coefficients are calculated for the real, complex geometric shape

Asteroids • Realistic breakup Intro Methods Our Activ. • Shadowing

23-June-15 Second talk at University of Cagliari 72 Space Debris Re-entry

• SCARAB is a multi-disciplinary analysis tool which Entry Flows incorporates: Hyper. Flows • a CAD-like user interface to define the geometry, mass, and material properties of a complex spacecraft, • a 6 degrees-of-freedom (6 DoF) flight dynamics analysis to Space Debris predict the trajectory and attitude, Intro • an aerodynamic analysis to compute perturbing forces and Tools&Met. torques, Our Activ. • an aerothermal analysis to determine heat flux, • a thermal analysis to determine the heat balance in each part of the spacecraft, and Asteroids • a structural analysis to monitor local stress levels. Intro Methods • A break-up is initiated, if local stress limits are exceeded, or if Our Activ. load-bearing joints are molten.

23-June-15 Second talk at University of Cagliari 73 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • SCARAB has a graphical modelling system => completely panelised, consistent geometric model of the spacecraft • hierarchy levels, allowing the composition of complex system by Space Debris subsystems, compounds, elements and finally primitives Intro (elementary geometric shapes, e.g. spheres, cylinders, boxes) Tools&Met. as the lowest level Our Activ.

Asteroids Intro Methods Koppenwallner et Our Activ. All 2005

23-June-15 Second talk at University of Cagliari 74 Space Debris Re-entry • SCARAB Entry Flows Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids

Intro Lips and Fritsche, 2005 Methods Beppo Sax Our Activ. Koppenwallner et All 2005

23-June-15 Second talk at University of Cagliari 75 Space Debris Re-entry

• SCARAB Entry Flows

Hyper. Flows • The material database contains about 20 physical properties: Space Debris – temperature independent like density, melting temperature, and heat of melting. Intro – temperature-dependent like ultimate tensile strength, elasticity Tools&Met. module, specific heat capacity, thermal conductivity, and Our Activ. emission coefficient.

• From “monolithic, solid, metallic, and isotropic materials “ Asteroids to also “liquid or gaseous tank contents, non-metallic Intro ceramics, glasses or plastics, and orthotropic, multi- Methods layered composites (e.g. honeycombs, fibre reinforced Our Activ. plastics)”

23-June-15 Second talk at University of Cagliari 76 Space Debris Re-entry

• SCARAB Entry Flows Hyper. Flows • Liquid and gaseous tank contents modelled as virtual solids by using available material properties. • Tank contents are assumed as fixed and do not slosh Space Debris around in the tank. Intro • Melting temperature set very high to ensure no melting. Tools&Met. • Density from the volume of the tank and the mass of the Our Activ. content. (assumed constant until a possible tank bursting). Asteroids • Strength and elasticity are both zero, because a virtual Intro solid cannot take any forces. Methods • Heat capacity and thermal conductivity determined for Our Activ. the mean operating pressure of the tank.

23-June-15 Second talk at University of Cagliari 77 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • non-metallic materials difficult to treat because of their completely different destruction process at high

Space Debris temperatures Intro – Crystalline ceramics can be treated as metallic Tools&Met. materials, but their melting point depends on Our Activ. atmospheric conditions.

– Semi-crystalline glass ceramics and amorphous Asteroids glasses: no exact melting point can be defined Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 78 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • Problematic materials: plastics (also in composite form like carbon fibre reinforced plastic, CFRP).

Space Debris • do not melt at high temperatures, but destroyed in a Intro combination of sublimation, oxidation, and other Tools&Met. types of chemical reactions or decompositions at Our Activ. molecular level • equivalent resistance against thermal destruction Asteroids has to be defined by adapting melting temperature, Intro Methods heat of melting, heat capacity, thermal conductivity Our Activ. and emission coefficient.

23 -June-15 Second talk at University of Cagliari 79 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • Model orthotropic properties

• Honeycomb composites can be modelled, as long Space Debris as the honeycomb core and the sheet panels Intro consist of the same material. In this case, they can Tools&Met. be modelled as a monolithic material with reduced Our Activ. density and thermal conductivity • Each layer of the composites can also be modelled Asteroids separately using different materials Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 80 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • a spacecraft is composed of a large number of elementary geometric shapes, each with uniform

Space Debris material properties. Intro • All elementary shapes are discretized into volume Tools&Met. elements (voxels) with planar surface facets which Our Activ. are adjacent to a neighbouring voxel, or form a part of the outside or inside surface of the spacecraft. Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 81 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • At every other integration step the mass properties are re-evaluated, and the aerodynamic, aero-

Space Debris thermal, and thermal view factors of each voxel are Intro re-determined to account for attitude changes, Tools&Met. break-ups, or melting. Our Activ. • The perturbing aerodynamic forces and moments (translational and rotational accelerations) are Asteroids determined by a surface integral over all voxel Intro Methods surfaces which are exposed to the flow field of Our Activ. density ρ and aerodynamic velocity V .

∞

23-June-15 Second talk at University of Cagliari 82 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • Hypersonic approximations are used for the aerodynamic model (three flow regimes).

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods

Our Activ. (Lips and Fritsche, 2005)

23-June-15 Second talk at University of Cagliari 83 Space Debris Re-entry

• SCARAB Entry Flows Hyper. Flows • Free molecular flow: σ 2 −σ 1 T  c = N N Π(S )+ w χ(S ) Space Debris p, fm 2  n n  π S∞  σ N 2 T∞  Intro Tools&Met. σ c = τ sin(θ )χ(S ) Our Activ. τ , fm 2 n π S∞

• S∞ = , is the free-stream molecular speed ratio Asteroids 푉∞ Sn=S∞cos( ) is its normal component to an inclined 2푅푇∞ Intro surface� element, Π and χ are some functions of Sn., and Methods T∞ is free stream휃 the temperature, let Tw and θ are the Our Activ. local wall temperature and incidence angle

23-June-15 Second talk at University of Cagliari 84 Space Debris Re-entry

• SCARAB Schaaf and Chambre accommodation coefficients, σN and σ Entry Flows accommodate the incident and reflected energies. Hyper. Flows 휏 • Free molecular flow: σ 2 −σ 1 T  c = N N Π(S )+ w χ(S ) Space Debris p, fm 2  n n  π S∞  σ N 2 T∞  Intro Tools&Met. σ c = τ sin(θ )χ(S ) Our Activ. τ , fm 2 n π S∞

23-June-15 Second talk at University of Cagliari 85 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows

• Hypersonic continuum flow Space Debris • Modified Newtonian approach Intro Tools&Met. • For wetted surfaces ( < /2 ) Our Activ. 2 c p,cont = kN1(γ , M ∞ ,휃θ )cos휋 (θ )+ kN 2 (γ , M ∞ ,θ )

cτ = 0 Asteroids ,cont Intro Methods • is the specific heats ratio Our Activ. 훾

23-June-15 Second talk at University of Cagliari 86 Space Debris Re-entry

Entry Flows • In particular the local pressure and shear stress Hyper. Flows coefficients cp and cτ can be determined for each of the re-entry flow regimes according to:

Space Debris • Transition by bridging Intro Tools&Met. c p,trans = c p,cont + (c p, fm − c p,cont )f p (Kn∞,s ) Our Activ. cτ = cτ + (cτ − cτ )fτ (Kn∞ ) ,trans ,cont , fm ,cont ,s

Asteroids • Kn∞,s is based on free stream density and stagnation Intro point temperature and viscosity. Methods Our Activ.

23-June-15 Second talk at University of Cagliari 87 Space Debris Re-entry

• SCARAB Entry Flows • These models are applied locally to the panels of the Hyper. Flows geometric model.

• Integral force and torque coefficients are calculated from the resulting pressure and shear stress distribution over Space Debris the spacecraft surface. Intro Tools&Met. Our Activ. • The aero-thermal analysis predicts the convective heat transfer to the outer surface of the spacecraft based on Asteroids the aerodynamic conditions. Intro • Like the aerodynamic coefficients, the heat transfer is Methods computed as a combination of the free molecular and Our Activ. continuum values

23-June-15 Second talk at University of Cagliari 88 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows α q St = = ρVc ρVc ∆T Space Debris p p Intro Tools&Met. • Free molecular heating St fm,s ≈1 Our Activ. • “Stanton number computed with standard approach

equivalent to pressure and shear stress coeff. Asteroids 2.1 Stcont = (0.1+ 0.9cosθ ) Intro Re∞,s Methods • Continuum ρ Power law viscosity dependence on Our Activ. ∞V∞ RN Re∞ = temperature ,s µ(T ) s

23 -June-15 Second talk at University of Cagliari 89 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods 230 83 Our Activ. 퐻 ≈ 푘� 퐻 ≈ 푘�

23-June-15 Second talk at University of Cagliari 90 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • The thermal analysis is based on a two- dimensional heat conduction model (radial or

Space Debris lateral neighbouring panels). Intro Tools&Met. Our Activ. Destruction by melting is analysed on panel level. Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 91 Space Debris Re-entry

Entry Flows • SCARAB Hyper. Flows • Angle of attack and bank angle variation (constant lift-to-drag ratios) is used for Ma<6 within the

Space Debris supersonic, transonic, and subsonic regime to Intro calculate the ground dispersion of the surviving Tools&Met. fragments. Our Activ.

• Several atmosphere models are available, Asteroids Intro including US Standard 1976, MSISe-90, MSISe- Methods 00, Jacchia-71 Our Activ.

23-June-15 Second talk at University of Cagliari 92 Space Debris Re-entry

Entry Flows • COMPARISON of ORSAT and SCARAB Reentry Hyper. Flows Analysis Tools for a Generic Satellite Test Case (extracted from Kelley et All, Bremen, 2010)

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 93 Space Debris Re-entry

Entry Flows • COMPARISON of ORSAT and SCARAB Reentry Hyper. Flows Analysis Tools for a Generic Satellite Test Case (extracted from Kelley et All, Bremen, 2010)

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 94 Space Debris Re-entry

Entry Flows • COMPARISON of ORSAT and SCARAB Reentry Hyper. Flows Analysis Tools for a Generic Satellite Test Case (extracted from Kelley et All, Bremen, 2010)

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 95 Space Debris Re-entry

• DEBRISK, a Tool for Re-Entry Risk Analysis Entry Flows Hyper. Flows • Developed by CNES from 2008 • Object based approach • Similar to ORSAT Space Debris Intro Tools&Met. • DEBRIS Our Activ. • within the DEIMOS Planetary Entry Toolbox • estimates the footprint on ground of the debris of an uncontrolled re-entry object Asteroids Intro • give a first shot of the impact area of the debris produced Methods by a vehicle break-up during its atmospheric entry, Our Activ. exploring also the survivability of the elements

23-June-15 Second talk at University of Cagliari 96

An Open-Source Hypersonic Aerodynamic and Aerothermodynamic Modeling Tool

Piyush M. Mehta, Edmondo Minisci, Massimiliano Vasile University of Strathclyde, United Kingdom

Andrew Walker Los Alamos National Laboratory, United States

Melrose Brown University of New South Wales at ADFA, Australia

Motivation

Entry Flows • FOSTRAD: Free Open Source Tool for Re- Hyper. Flows entry of Asteroids and Debris

• Current Tools are proprietary (ORSAT-NASA Space Debris and SCARAB-ESA) or not open-source (DAS- Intro NASA, DRAMA-ESA) Tools&Met. Our Activ. • Tools do not perform Uncertainty Quantification or Probabilistic Modeling • Simple Tools exist for Asteroids Asteroids Intro • Literature is not accurate or adequate Methods Our Activ.

23-June-15 Second talk at University of Cagliari 98

Objectives

Entry Flows • To develop and implement high fidelity models to Hyper. Flows predict aero-thermal characteristics of re-entry objects (both debris and asteroids)

Space Debris Intro • To characterize involved uncertainties and to Tools&Met. investigate how uncertainties evolve through Our Activ. models

Asteroids Intro • To integrate aero-thermal and uncertainty Methods quantification models into trajectory simulation Our Activ. environment

23-June-15 Second talk at University of Cagliari 99 Introduction: Multi-Fidelity Approach

Entry Flows • The tool is based on panel method which divides Hyper. Flows and models objects (spacecraft or debris) with a triangular mesh

Space Debris • Aerodynamic and Thermal loads on each Intro element are calculated using analytical and Tools&Met. empirical methods Our Activ. • Currently, we – Validate aerodynamic computations, Asteroids – Present development of new aerodynamic bridging Intro functions, and Methods Our Activ. – Compare different analytical/semi-empirical aerothermodynamic models with CFD and DSMC

23-June-15 Second talk at University of Cagliari 100 Aerodynamics

Entry Flows • Modified Newtonian Theory in the continuum regime Hyper. Flows and flat plate analytical formula by Schaaf and Chambre for free molecular flow

Space Debris Continuum Free-Molecular Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 101 Results: Aerodynamics Bridging Formula

Entry Flows • We use a more flexible basis function, Hyper. Flows sigmoid (base 10), to track the data more accurately

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 102 Results: Aerodynamics Bridging Formula

Entry Flows Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 103 Aerothermodynamics

Detra-Kemp-Riddell (as used in SCARAB), Fay Riddell, Entry Flows and Van Driest in the continuum regime and analytical Hyper. Flows model for free molecular regime Continuum Free-Molecular

Space Debris DKR: Intro Tools&Met. Our Activ. FR:

Asteroids VD: Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 104 Aerothermodynamics: Bridging and Distribution

Entry Flows • The bridging formula by Legge is used for Hyper. Flows computations in the transition region

Space Debris Intro Tools&Met. Our Activ. • The distribution on the body is calculated using the model used in SCARAB

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 105 Stagnation Point Heat Transfer for Orion

– High fidelity simulations use CFD in the Continuum Regime and Entry Flows DSMC in transition regime Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 106 Conclusions

Entry Flows • Validated Aerodynamic computations in the free Hyper. Flows molecular and continuum regime

Space Debris • Developed new bridging functions for aerodynamic Intro coefficients that allow better tracking of the data Tools&Met. Our Activ. • Compared High fidelity and low fidelity

Asteroids aerothermodynamics for an understanding of the Intro uncertainties Methods Our Activ.

23-June-15 Second talk at University of Cagliari 107

Preliminary study of uncertainty propagation for reentry of orbital debris

Martin Kubicek, Edmondo Minisci University of Strathclyde, Glasgow, Scotland Monte Carlo Sampling

Entry Flows • Monte Carlo methods (or Monte Carlo Hyper. Flows experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in Space Debris Intro physical and mathematical problems and are most Tools&Met. useful when it is difficult or impossible to use other Our Activ. mathematical methods. Monte Carlo methods are

mainly used in three distinct problem classes: Asteroids optimization, numerical integration, and generating Intro draws from a probability distribution. (Wikipedia) Methods Our Activ.

23-June-15 Second talk at University of Cagliari 109 Monte Carlo Sampling

Entry Flows • Monte-Carlo (MC) for Uncertainty Propagation, Hyper. Flows basically follows three main steps: 1. sample the input random variable(s) from their known or assumed (joint-) Probability Density Function (PDF), Space Debris 2. compute deterministic output for each sampled input Intro Tools&Met. value(s), and Our Activ. 3. determine the statistical characteristics of the output distribution (e.g. mean, variance, skewness).

Asteroids Intro • The MC method has the property that it converges to Methods the exact stochastic solution when the number of Our Activ. samples n→∞.

23-June-15 Second talk at University of Cagliari 110 Entry Flows Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 111 Derivative Approach - scheme Non - Intrusive Uncertainty Quantification Entry Flows Hyper. Flows  For each sub-space, a separate interpolation strategy is used

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro  For each sub-space, a separate sampling strategy is use Methods Our Activ.

23-June-15 Second talk at University of Cagliari 112 Martin Kubicek 24/06/2015 112 Introduction – Problem definition

Entry Flows Debris re-entry Hyper. Flows Problem set: Debris re-entry from a low earth orbit (90 Km) to the earth Space Debris ground (assumed sea level). The orbit is set to be Intro equatorial, where the trajectory is considered only 2D and Tools&Met. disturbances perpendicular to the plane are neglected. Our Activ. However, the yaw angle is considered uncertain in the last

case. The starting position is at longitude 0 and latitude 0,

Asteroids where the starting velocity is 7600 km/s and the direction is Intro east. The mass of the asteroid is assumed 250 kg. The Methods starting velocity and mass are considered uncertain in the Our Activ. last case.

23-June-15 Second talk at University of Cagliari 113

Introduction – Distributions

Conditions Entry Flows Hyper. Flows Case 4 – 16D:

Random Variable Distrib. Mean Std. Central Point Space Debris Temperature at 0 km [K] Gumbell 281.7 14.05 281 Intro Temperature at 20 km [K] Gumbell 216.8 7.04 217 Tools&Met. Temperature at 50 km [K] Landau 266.5 14.95 266 Our Activ. Temperature at 70 km [K] Landau 224.3 18.90 224.3

Temperature at 90 km [K] Gaussian 184.9 25.11 184.9

Temperature at 120 km [K] Gaussian 359.9 24 359.9 Asteroids Density at 0 km [g·m−3] Gaussian 1225 81.667 1225 Intro Density at 40 km [g·m−3] Gaussian 4 0.533 4 Methods Density at 90 km [g·m−3] Gaussian 0.003416 0.00056933 0.003416 Our Activ. Density at 120 km [g·m−3] Gaussian 0.00002222 0.00000370333 0.00002222

Chemical composition is considered N2O2

23-June-15 Second talk at University of Cagliari 114

Introduction – Distributions

Entry Flows Hyper. Flows Case 4 – 16D:

Conditions Space Debris Intro Random Variable Distrib. Min Max Central Point Tools&Met. Percentage of N [%] Uniform 0.784 0.816 0.8 Our Activ. 2 Heat capacity (cp) [J·K−1] Uniform 1304.35 1441.65 1373

Path angle at entry Uniform 0 -2.5 -1.25

[Degrees] Asteroids Speed of entry [m/s] Uniform 7410 7790 7600 Intro Mass of debris [Kg] Uniform 243.75 256.25 250 Methods Angle of azimuth [deg] Uniform 87.50 92.5 90.00 Our Activ.

Chemical composition is considered N2O2

23-June-15 Second talk at University of Cagliari 115 Introduction – Distributions Conditions

Entry Flows Hyper. Flows Case 4 – 16D:

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 116

Solution – Output Distribution Reentry - distribution

Entry Flows The output position is calculated in a following way: Hyper. Flows =

where f(x) is the output of reentry code and it represents a longitude angle (rad) and Re is the radius of earth. 푦 � 풙 ∗ 푅푅 Space Debris Mean Std Intro Case 3 – 16D Tools&Met. Number of simulations: 277* 2592174.80 869055.22

Our Activ. 59.09 69489.77

Asteroids Intro Methods Our Activ.

* Low number of samples is due to neglecting the non-important interaction effects

23-June-15 Second talk at University of Cagliari 117

Solution – Output Distribution Reentry - distributions • Introduction Case 4 – 16D Entry Flows Number of simulations: 277* Hyper. Flows • Problem definition

• Distributions Space Debris • Methodology Intro Tools&Met. • Solution Our Activ. • Output Distribution

• Problem definition Asteroids • Sensitivity results Intro

Methods Our Activ.

* Low number of samples is due to neglecting the non-important interaction effects

23-June-15 Second talk at University of Cagliari 118

Solution – Sensitivity results Output 1 - X Sensitivity table – 16D case

Random Variable Partial Mean Partial Variance Mean sensitivity Variance sensitivity

1 0.033617 0.02293 1.5419e-07 3.8794e-14 Entry Flows 2 -0.00090148 25.3359 4.1348e-09 4.2865e-11 Hyper. Flows Case 3 1 – 9D-0.10475: 215.776 4.8046e-07 3.6507e-10

4 -0.28146 10.1754 1.291e-06 1.7215e-11 5 -0.021961 0.3535 1.0073e-07 5.9808e-13 Space Debris 6 0.0010471 0.071433 4.8028e-09 1.2086e-13 7 0.15193 12.1984 6.9684e-07 2.0638e-11 Intro 8 1075.6023 203017426.9862 0.0049334 0.00034348 Tools&Met. 9 588.3531 76461215.5724 0.0026986 0.00012936 Our Activ. 10 25.5439 148775.258 0.00011716 2.5171e-07

11 -0.00046689 0.10161 2.1414e-09 1.7191e-13 12 -3.1247 11003.2883 1.4332e-05 1.8616e-08

13 135315.4107 430498051281.1843 0.62065 0.72835 Asteroids 14 40334.2701 '65189233208.6528 0.185 0.11029 Intro 15 -22.4706 7031855.4075 0.00010307 7.6734e-07 Methods 16 -751.192 453545.9359 0.0034455 2.1688e-08

Our Activ. Interaction – 13,14 39634.219 95041290036.0517 0.18179 0.00047719 Interaction – 9,14 104.5167 25188155.5754 0.00047938 4.2615e-05 Interaction – 9,13 8.4624 8782424.1463 3.8814e-05 1.4859e-05

23-June-15 Second talk at University of Cagliari 119

Solution – Sensitivity results Output 2 - Y Sensitivity table – 16D case

Random Variable Partial Mean Partial Variance Mean sensitivity Variance sensitivity

Entry Flows 1 2.0585e-18 8.5973e-35 2.7664e-20 2.0649e-44 2 -5.52e-20 9.4994e-32 7.4185e-22 2.2815e-41 Hyper. Flows Case 3 1 – 9D-6.4142e: -18 8.0903e-31 8.6203e-20 1.9431e-40

4 -1.7235e-17 3.8152e-32 2.3162e-19 9.1631e-42 5 -1.3447e-18 1.3254e-33 1.8072e-20 3.1834e-43 Space Debris 6 6.4118e-20 2.6783e-34 8.6171e-22 6.4327e-44 7 9.3028e-18 4.5736e-32 1.2502e-19 1.0985e-41 Intro 8 6.5862e-14 7.6119e-25 8.8514e-16 1.8282e-34 Tools&Met. 9 3.6026e-14 2.8668e-25 4.8417e-16 6.8855e-35 Our Activ. 10 1.5641e-15 5.5782e-28 2.1021e-17 1.3397e-37

11 -2.8588e-20 3.8096e-34 3.8421e-22 9.1499e-44 12 -1.9133e-16 4.1256e-29 2.5714e-18 9.9087e-39

13 8.3406e-12 1.6186e-21 1.1209e-13 3.8876e-31 Asteroids 14 2.6051e-12 2.486e-22 3.501e-14 5.9708e-32

Intro 15 -1.3759e-15 2.6365e-26 1.8492e-17 6.3323e-36

Methods 16 -6.8046 3736730837.7348 0.091449 0.89748 Interaction – 14,16 15.0852 53378456.2397 0.20274 0.01282 Our Activ. Interaction – 13,16 50.5845 373265293.6149 0.67983 0.08965 Interaction – 8,16 0.44174 162771.279 0.0059367 3.9094e-05

23-June-15 Second talk at University of Cagliari 120

Solution – Sensitivity results Sensitivity Histograms – 16D case

Output 1 - X Entry Flows Case 1 – 9D: Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Output 2 - Y Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 121 (C) Shutterstock

ASTEROID ENTRY Asteroid Entry

Entry Flows • Complex and coupled physical phenomena such as Hyper. Flows hypersonic aerodynamics, heating, ablation, fragmentation, fragments interaction, and airburst.

Space Debris • Asteroid are characterised by very high kinetic Intro energy levels. Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 123 Asteroid Entry

Entry Flows • The strength is defined by impactor composition and Hyper. Flows structure and varies with meteoroid size [Weibull, 1951].

Space Debris • In general, the falling body (or each of its fragment) Intro is not homogeneous, and the fragmentation occurs Tools&Met. near the "weak" points (cracks or other defects). Our Activ. • Each fragmentation leads to a decrease in the defect number and an increase in the sub-fragment Asteroids strength. Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 124 Asteroid Entry

• Several differences between the planetary entry of space debris Entry Flows and of asteroids: Hyper. Flows – object properties and entry conditions not known/partially known, with high level of uncertainty. Space Debris – approaches to predict the thermal loads must be different due to Intro much higher velocities involved (up to 70 km/s); Tools&Met. – the mechanism of the fragmentation is quite different, (more due to Our Activ. mechanical loads than thermal ones for asteroids)

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 125 Asteroid Entry

• The fall of a meteorite begins when it enters the upper Entry Flows atmosphere. Its initial geocentric velocity can range from l l.2 to Hyper. Flows -1 about 70 km s assuming the meteoroid to be in a heliocentric orbit. Space Debris • Its entry angle can also range from near 0 to 90 [deg] with Intro respect to the local horizon, with 45 [deg] being the most likely Tools&Met. entry angle Our Activ.

Asteroids Intro (Passey and Melosh, 1980) Methods Our Activ.

23-June-15 Second talk at University of Cagliari 126 Asteroid Entry

• As the meteoroid collides with atoms in the air, some of its Entry Flows kinetic energy is dissipated. Hyper. Flows • Some of this energy is used in ablating the body by melting and/or vaporizing the exposed surface. Space Debris • Some of its momentum is also transferred to the air and the Intro resultant atmospheric drag decelerates the meteoroid. Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 127 Asteroid Entry

Entry Flows Atmospheric entry can be described by simplified Hyper. Flows differential equations for • a point mass without disruption (McKinley 1961), or with a simplified treatment of disruption, either Space Debris – the Separate Fragments (SF) model (Passey and Melosh Intro 1980; Artemieva and Shuvalov 1996, 2001), or Tools&Met.

Our Activ.

Asteroids Intro Methods Our Activ. – the pancake model (Chyba et al. 1993).

23-June-15 Second talk at University of Cagliari 128 Asteroid Entry

• The alternative to the simplified approach is to use 4) full-scale Entry Flows hydrodynamic models in which the projectile is treated as a Hyper. Flows strengthless continuous body (Ahrens et al. 1994; Takata et al. 1994;Crawford et al. 1995), as a body with some kind of Space Debris strength (Ivanov and Melosh 1994), or as a cloud of fragments Intro (Svetsov et al. 1995). Tools&Met. Our Activ.

Artemieva & Asteroids Pierazzo 2009 Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 129 Asteroid Entry

• Since the internal properties of comets and asteroids are Entry Flows poorly known, simplified approaches are competitive with Hyper. Flows more comprehensive hydrodynamic models because they allow to investigate systematically a wide range of input parameters over a short period of time. Space Debris • However, depending on the approximation used, the final Intro results (fragments’ masses, their velocities) may differ by Tools&Met. an order of magnitude. Our Activ. • Under the same initial conditions the no-disruption regime will provide maximum pre-impact velocity (minimum pre- Asteroids atmospheric mass for reverse studies), while the pancake Intro model with infinite projectile spreading will provide Methods minimum pre-impact velocity (maximum pre-atmospheric Our Activ. mass for reverse studies).

23-June-15 Second talk at University of Cagliari 130 Asteroid Entry

• Models: solid, non deformable body Entry Flows • The projectile motion in the atmosphere is described by a Hyper. Flows set of differential equations ablation for the point mass, taking into account drag, gravity, and (for example, Melosh 1989; Chyba et al. 1993): Space Debris dV ρ AV 2 = −C a + g sin(θ ) Intro dt D 2m Tools&Met. dm C ρ V 3 Our Activ. = −A H a dt 2Q

• where V is the velocity [m/s], t = time [s], CD and CH = Asteroids drag and heat transfer coefficients, ρa = atmospheric -3 2 Intro density [kg m ], A = cross-sectional area of the body [m ], -2 Methods m = its mass [kg], g = gravity acceleration [m s ], Q = -1 Our Activ. heat of ablation [J kg ], [K], and θ = path angle [deg].

23-June-15 Second talk at University of Cagliari 131 Asteroid Entry

• Models: solid, non deformable body Entry Flows Hyper. Flows • Combined with simple kinematical equations for

dθ g cos(θ ) • flight path angle = Space Debris dt V Intro dZ Tools&Met. • altitude = −V sin(θ ) Our Activ. dt dX • ground distance = V cos(θ ) dt Asteroids Intro • previous equations result in reasonably accurate Methods predictions for the trajectory of a meteoroid that travels Our Activ. through the atmosphere without breaking up.

23-June-15 Second talk at University of Cagliari 132 Asteroid Entry

Entry Flows • Models: solid, non deformable body Hyper. Flows

dθ g cos(θ ) V cos(θ ) = − Space Debris dt V RE + Z Intro dX V cos(θ ) Tools&Met. = dt 1+ Z / R Our Activ. E

Asteroids • where RE is the Earth’s radius Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 133 Asteroid Entry

Entry Flows • Models: solid, non deformable body Hyper. Flows dm C ρ V 3 = −A H a dt Q Space Debris Intro Tools&Met. • From observations: 0.1 for altitude > 30km Our Activ. 퐻 3  퐶 C≈H ρaV 4 min , σ SBT  dm  2  = −A Asteroids dt Q Intro where V is the velocity, t = time, CH is the heat transfer coefficient, ρa = Methods atmospheric density, A = crosssectional area of the body, m = its mass, Q = Our Activ. heat of ablation, σSB = Stephan-Boltzmann constant, and T = temperature.

23-June-15 Second talk at University of Cagliari 134 Asteroid Entry

Separate Fragments (SF) model Entry Flows Hyper. Flows • Hypothesis of the disruption of an impactor traveling through the atmosphere can be traced back to Barringer’s early studies of Meteor Crater on early ‘900 Space Debris • Actual importance of atmospheric disruption for small Intro bodies (up to a few hundred meters in diameter) was Tools&Met. realized only much later. Our Activ. • First analytical study, based on observations of terrestrial

crater strewn fields, was carried out by Passey and

Asteroids Melosh (1980). Intro – Evolution of a disrupted body as a two-stage process: Methods • 1) a strong but short interaction of the fragments immediately after the disruption, followed by Our Activ. • 2) the motion of individual fragments.

23-June-15 Second talk at University of Cagliari 135 Asteroid Entry

Entry Flows • Models: Separate Hyper. Flows Fragments

• Repulsion of fragments Space Debris in separated fragment Intro (SF) models, caused by Tools&Met. the interaction of bow Our Activ. shocks (Passey and Melosh 1980; Artemieva Asteroids and Shuvalov 1996). Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 136 Asteroid Entry

Entry Flows • Models: Separate Hyper. Flows Fragments

• Original formulation of Space Debris Passey and Melosh 1980: Intro Tools&Met. • Immediately after Our Activ. fragmentation, the meteoroid fragments travel as a unit within a single Asteroids Intro bow shock. Methods Our Activ.

23-June-15 Second talk at University of Cagliari 137 Asteroid Entry

Entry Flows • Models: Separate Fragments Hyper. Flows • Original formulation of Passey

and Melosh 1980: Space Debris • Soon afterwards the fragments Intro become sufficiently separated Tools&Met. Our Activ. that they have individual bow shocks. High pressures develop between these bow Asteroids shocks, producing an Intro Methods acceleration transverse to the Our Activ. trajectory of the incoming meteoroid

23-June-15 Second talk at University of Cagliari 138 Asteroid Entry

• Entry Flows Models: Separate Fragments Hyper. Flows • Original formulation of Passey and Melosh 1980:

Space Debris • finally, the interaction of the bow Intro shocks and the transverse Tools&Met. acceleration cease, leaving the Our Activ. fragments to travel in their modified trajectories (V1 and Asteroids V2). Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 139 Asteroid Entry

• Models: Separate Fragments Entry Flows Hyper. Flows • Original formulation of Passey and Melosh 1980:

Space Debris • assuming that the bow shocks Intro exert a force on each other Tools&Met. until the two meteoroid Our Activ. fragments have a separation of a certain number C of 훽 Asteroids meteoroid radius R1, Intro Methods = C R1 Our Activ. • time of interaction  2β  훽 ∆t =   (a=acceleration)  a 

23-June -15 Second talk at University of Cagliari 140 Asteroid Entry

• Models: Separate Entry Flows Hyper. Flows Fragments • Original formulation of Passey and Melosh 1980: Space Debris Intro • The final transverse Tools&Met. velocity VT is Our Activ. VT = a∆t = 2βa

2 2 2 ρaVi πR2 3ρaVi Asteroids a = F = = m 4 πR3ρ 4ρ R Intro 3 2 m m 2 Methods Our Activ. 3 R1 ρa VT = 2βa = Vi C 2 R2 ρm

23-June-15 Second talk at University of Cagliari 141 Asteroid Entry

• Models: Separate Entry Flows Hyper. Flows Fragments • Original formulation of Passey and Melosh 1980: Space Debris • By studying the cross-range Intro spread of craters in known Tools&Met. crater fields, it is possible to Our Activ. determine an approximate value of the constant C

Asteroids • Using the information on Intro cross-range spreads, the Methods constant C is calculated to be Our Activ. between 0.02 and 1.52

23 -June-15 Second talk at University of Cagliari 142 Asteroid Entry

Separate Fragments (SF) model Entry Flows Hyper. Flows • Passey and Melosh’s analytical model was translated into a numerical model by Artemieva and Shuvalov (1996, 2001), and was named the Separate Fragments (SF) model. Space Debris • The SF model has been applied to a wide range of impactor Intro (pre-atmospheric) masses by Bland and Artemieva (2003, Tools&Met. 2006). Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 143 Asteroid Entry

Entry Flows Separate Fragments (SF) model Hyper. Flows • The SF model considers successive fragmentations and ablations of individual fragments (where the

Space Debris number of fragments, N =1 at the start, and , N 1 Intro at the end). Tools&Met. ≫ • A meteoroid is disrupted into a pair of fragments Our Activ. whenever the dynamic loading exceeds its strength, which depends on the meteoroid type and size. Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 144 Asteroid Entry

Separate Fragments (SF) model Entry Flows • Fragment mass and direction of separation (the two fragments Hyper. Flows move away from each other in opposite directions) are defined at random. • Immediately after the breakup, fragments tend to have a higher Space Debris strength than the parent body, but can be disrupted again into a new pair later on, when the dynamic loading exceeds the Intro fragments’ strength. Tools&Met. • Each fragmentation leads to a decrease in the defect number and Our Activ. an increase in the sub-fragment strength.

• the strength σf of the sub-fragment with mass mf is determined by the relation [Weibull, 1951], Asteroids • = 0.25 푎 Intro 푚0

Methods 휎푓 휎0 푚푓 � ≈ Our Activ. • where σ0 and m0 are the initial parent meteoroid strength and mass.

23-June-15 Second talk at University of Cagliari 145 Asteroid Entry

Separate Fragments (SF) model Entry Flows Hyper. Flows • The model is most applicable for bodies smaller than a few meters in diameter; for larger bodies the basic assumption of “separation” among fragments becomes quickly invalid. Space Debris • In this case, a dense cloud of fragments tends to decelerate as Intro a cloud, not as individual particles. Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 146 Asteroid Entry

• Models: pancake Entry Flows • Equation, which describe the spreading of a disrupted body in Hyper. Flows the pancake models of Chyba et al. (1993) and Hills and Goda

(1993):

Space Debris Intro Tools&Met. Our Activ.

V Asteroids 2 2 d r ρaV Intro r = C 2 D ρ Methods dt m -3 Our Activ. • where r is the projectile radius [m] and ρm is its density [kg m ]

23-June-15 Second talk at University of Cagliari 147 Asteroid Entry

Entry Flows Pancake model Hyper. Flows • Zahnle 1992; Chyba et al. 1993; Hills and Goda 1993; Collins et al. 2005.

Space Debris • This simple analytical model treats the disrupted Intro meteoroid as a deformable continuous fluid. Tools&Met. Our Activ. • Used to describe comet-like and stone meteoroids, • Application to irons is questionable.

Asteroids • Many uncertainties and “ad hoc” choices, such us Intro the maximum allowed radius of pancaking. Methods Our Activ.

23-June-15 Second talk at University of Cagliari 148 Asteroid Entry

Pancake model Entry Flows Hyper. Flows • In the original model (Zahnle 1992), there were no restrictions on the growth of the pancake radius, leading to unrealistically thin and wide projectiles and to Space Debris extremely low final velocities. Intro Tools&Met. • Numerical models carried out around the same time that Our Activ. the pancake model was developed clearly showed that

although flattening (“pancaking”) is a typical behaviour of

Asteroids disrupted projectiles, it is mostly restricted to a flattening Intro factor of 1.7–2.3. Methods (Ivanov et al. 1992; Ahrens et al. 1994; Takata et al. 1994; Crawford et al. 1995) Our Activ.

23-June-15 Second talk at University of Cagliari 149 Asteroid Entry

Pancake model Entry Flows • Further, widening is arrested by the growth of Kelvin- Hyper. Flows Helmholtz (K-H) and Rayleigh-Taylor (R-T) instabilities and the resulting projectile fragmentation.

• However, commonly used restrictions on the maximum Space Debris spread of the object (above 2) are purely artificial. Intro Tools&Met. • Different choices of the object’s maximum spread can lead to substantially different results even for identical Our Activ. initial conditions.

• The pancake model does not describe the object behaviour after maximum spreading is reached (would Asteroids the object keep its shape and mass or would only some Intro part of its mass reach the surface, while the rest Methods fragments and disappears in the atmosphere?). Our Activ.

23-June-15 Second talk at University of Cagliari 150 Asteroid Entry

Pancake model Entry Flows • Large fragments may escape the cloud and continue flight as Hyper. Flows independent bodies. • The pancake model has been reproduced by adding minor modifications to the SF model (Artemieva&Pierazzo 2009). Space Debris • This was possible because the pancake model utilizes the Intro same equations of motion for an intact body used by the SF Tools&Met. model (Melosh 1989, p. 206–207), with only an additional Our Activ. equation for spreading (Chyba et al. 1993).

• Neither the pancake model nor the SF model are realistic Asteroids models for the evolution of some projectiles such as the one that produced the Canyon Diablo. An accurate reproduction of Intro this event requires the application of full-scale hydrodynamic Methods modelling. Our Activ.

23-June-15 Second talk at University of Cagliari 151 Asteroid Entry

Hydrodynamic codes Entry Flows • The best solution for an accurate investigation of impactor Hyper. Flows disruption in the atmosphere is through direct numerical modelling of the atmospheric entry.

• too expensive for systematic studies, considering that Space Debris small bodies must be followed through distances Intro exceeding by far their diameter (~50m versus 20–50 km). Tools&Met. • This causes obvious computation cost versus resolution Our Activ. issues, especially considering that internal properties of incoming objects (shape, strength, porosity, homogeneity) are still poorly known. This approach, therefore, can only Asteroids be used for investigating a few test cases, after a more Intro systematic investigation has been carried out with the Methods simpler models. Our Activ.

23-June-15 Second talk at University of Cagliari 152 Asteroid Entry

Entry Flows New developments Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

3 r1 ρa Asteroids VT = V C 2 r2 ρm Intro Methods • does not adequately predict the separation Our Activ. behaviour of unequally sized bodies (Laurence, et All 2012)

23-June-15 Second talk at University of Cagliari 153 Asteroid Entry

Entry Flows New developments Hyper. Flows • The original assumption was: purely lateral separation • Actually: the smaller (secondary) body is subject to a

higher axial acceleration and thus travels both laterally Space Debris Intro and downstream relative to the larger (primary) body. Tools&Met. • “shock-wave surfing”: the secondary body traces a Our Activ. trajectory so as to follow the bow shock of the primary body downstream.

Asteroids • significantly larger lateral velocity because the interacting Intro flow field produces a substantial repulsive lateral force on Methods the secondary body. Our Activ. (Laurence, et All 2012)

23-June-15 Second talk at University of Cagliari 154 Asteroid Entry

Entry Flows New developments Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ. (Laurence, et All 2012)

23-June-15 Second talk at University of Cagliari 155 Asteroid Entry

Entry Flows New developments Hyper. Flows

Space Debris Intro Tools&Met. Our Activ. M

Asteroids Intro Methods 3 r ρ V 3 r V = V C 1 a V ' = T = C 1 Our Activ. T 2 r ρ T ρ 2 r 2 m V a 2 (Laurence, et All 2012) ρm

23-June-15 Second talk at University of Cagliari 156

BREAK-UP MODELING AND TRAJECTORY SIMULATION UNDER UNCERTAINTY FOR ASTEROIDS

Piyush M. Mehta, Edmondo Minisci, Massimiliano Vasile University of Strathclyde, United Kingdom

Presented at Planetary Defense Conference, Frascati, 2015 Introduction

Entry Flows • Development and results from the asteroid Hyper. Flows atmospheric entry plugin: – Ablation – Evaporation Space Debris – Successive/progressive fragmentation Intro – Pre- and post- fragmentation trajectory simulation Tools&Met. – Probabilistic ground impact distribution Our Activ. • Conservative approach under assumption that airbursts results in almost complete evaporation

Asteroids • Secondary effects are not presently considered Intro • Rapid, conservative solution for decision-making and Methods mitigation or casualty avoidance. Our Activ.

23-June-15 Second talk at University of Cagliari 158 Methodology

• 10,000-member Monte Carlo run with a large number Entry Flows of uncertain parameters Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 159 Methodology: Trajectory Dynamics Model

Entry Flows • Based in the Earth fixed spherical coordinate system Hyper. Flows under only the influence of drag.

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 160 Methodology: Hypersonic Aerodynamics

Entry Flows • We use a simple sphere model and a CD of 0.92 as Hyper. Flows nominal value given by Modified Newtonian Theory.

Space Debris Intro • Density is computed using an interpolation routine Tools&Met. developed using the US standard atmosphere Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 161 Methodology: Ablation Model

• Ablation due to both convective and radiative heat Entry Flows transfer are modeled. Hyper. Flows

Space Debris • Brandis et al., 2014, give convective and radiative Intro heat flux correlations as a function of density and Tools&Met. velocity Our Activ. Heat Flux Velocity Density

3 Convective (Brandis, et al,. 2014) 3 to 17 km/s 5e-3 to 1e-5 km/m Asteroids Radiative (Brandis, et al,. 2014) 9.5 to 17 km/s 5e-3 to 1e-5 km/m3 Intro Methods Convective (Fay-Riddell) 17 km/s and above All other densities Our Activ.

Radiative (Theoretical) 17 km/s and above All other densities

23-June-15 Second talk at University of Cagliari 162 Methodology: Ablation Model

• Fay-Riddell convective heat flux Entry Flows Hyper. Flows

• Radiative heat flux is computed using the theoretical model Space Debris Intro • Shock temperature computed by extrapolating Anderson data Tools&Met. • Total effective heat transfer to the spherical object is approximated Our Activ. based on high-fidelity CFD and DSMC simulations to be ~5% of stagnation point heat flux

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 163 Methodology: Successive Fragmentation

Entry Flows • Fragmentation is performed using the pressure Hyper. Flows differential model of Tsvetkov and Skripnik, 1991.

Space Debris • The material strength of the children post- Intro fragmentation is computed using the model of Tools&Met. Our Activ. Weibull, 1951.

Asteroids Intro Methods • The smaller fragment is assumed to be between Our Activ. 5 – 45% of the parent object by mass

23-June-15 Second talk at University of Cagliari 164 Methodology: Fragment Interaction Model

Entry Flows • Post fragmentation event, the larger child is assumed to Hyper. Flows continue along it path. The smaller child is given a lateral velocity computed using the model of Passey and Melosh

Space Debris Intro • We use the recently derived data of Laurence et al., 2012 to Tools&Met. Our Activ. compute the value of the parameter C

Asteroids Intro Methods diamond, M = 4; square, M = 6; circle, Our Activ. M = 10; triangle, M = 25

23-June-15 Second talk at University of Cagliari 165 Methodology: Uncertain parameters

Entry Flows Deterministic/N Parameter Distribution Min Value Max Value

Hyper. Flows ominal Value Entry Velocity (km/s) Uniform 20 15 25

Flight Path Angle, deg Uniform 15 10 20 Space Debris Direction Angle, deg Uniform 90 (due east) 89 91

Intro Initial Mass (kTon) Uniform 10 9 11 Tools&Met. Drag coefficient, CD Uniform 0.92 0.5 1.34 Our Activ. σ 2 Object strength, com (MN/m ) Uniform 20 10 30 Object density, (kg/m3) Uniform 3500 3000 4000

Asteroids Strength Scale factor, α Uniform 0.3 0.1 0.5 Intro Heat of ablation, (MJ/kg) Uniform 9 8 10 Methods Hot gas emissivity Uniform 0.05 0.01 0.09 Our Activ.

23-June-15 Second talk at University of Cagliari 166 Results: Flight path angle = -15 deg and ‘C’ model

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 167 Results: Flight path angle = -15 deg and ‘C’ model

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 168 Results: Flight path angle = -15 deg and ‘C’ model

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 169 Results: C = 0.1 (top) and C = 2.5 (bottom)

Entry Flows Hyper. Flows

Space Debris Intro Tools&Met. Our Activ.

Asteroids Intro Methods Our Activ.

23-June-15 Second talk at University of Cagliari 170 Results: C = 0.1 (top) and C = 2.5 (bottom)

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 171 Results: Flight path angle = -45 deg

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 172 Results: Flight path angle = -45 deg

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 173 Results: Flight path angle = -45 deg

Entry Flows Hyper. Flows

Space Debris

Intro Tools&Met. Our Activ.

Asteroids www.stardust2013.eu Intro twitter.com/stardust2013eu Methods Our Activ.

23-June-15 Second talk at University of Cagliari 174 Conclusions and Future Work

• Developed a tool for operational purposes that is freely Entry Flows available to anyone, including decision makers, should they Hyper. Flows choose to use it. Improvements in the implemented models can be easily integrated. Space Debris • The factor ‘C’ in the fragment interaction model is irrelevant for Intro our application when uncertainty in direction angle is taken into Tools&Met. account. Our Activ.

• Implement UQ-HDMR (High Dimensional Model

Asteroids Representation) approach to reduce the computational time by Intro 2 orders of magnitude (expected). Methods • Implement physics models for explosions and airbursts Our Activ. including secondary effect inference into the tool.

23-June-15 Second talk at University of Cagliari 175

Summary

Entry Flows • (Re-)Entry and Hypersonic Flows Hyper. Flows – Introduction to flow regimes and hypersonic phenomena (shock waves and heating)

23-June-15 Second talk at University of Cagliari 176 THANKS!

Edmondo Minisci ([email protected])

We will organise EUROGEN 2015

More info at www.strath.ac.uk/eurogen2015